Dynamical quantum jumps were initially conceived by Bohr as objective events associated with the emission of a light quantum by an atom. Since the early 1990s they have come to be understood as being associated rather with the detection of a photon by a measurement device, and that different detection schemes result in different types of jumps (or diffusion). Here we propose experimental tests to rigorously prove the detector dependence of the stochastic evolution of an individual atom. The tests involve no special preparation of the atom or field, and the required efficiency can be as low as η≈58%.
Dynamical quantum jumps were initially conceived by Bohr as objective events associated with the emission of a light quantum by an atom. Since the early 1990s they have come to be understood as being associated rather with the detection of a photon by a measurement device, and that different detection schemes result in different types of jumps (or diffusion). Here we propose experimental tests to rigorously prove the detector dependence of the stochastic evolution of an individual atom. The tests involve no special preparation of the atom or field, and the required efficiency can be as low as η≈58%.
It was recently argued (Wiseman and Gambetta 2012 Phys. Rev. Lett. 108 220402 ) that the stochastic dynamics (jumps or diffusion) of an open quantum system are not inherent to the system, but rather depend on the existence and nature of a distant detector. The proposed experimental tests involved homodyne detection, giving rise to quantum diffusion, and required efficiencies of well over 50%. Here we prove that this requirement ( ) is universal for diffusive-type detection, even if the system is coupled to multiple baths. However, this no-go theorem does not apply to quantum jumps, and we propose a test involving a qubit with jump-type detectors, with a threshold efficiency of only 37%. That is, quantum jumps are 'more quantum', and open the way to practical experimental tests. Our scheme involves a novel sort of adaptive monitoring scheme on a system coupled to two baths.
Experimental chapter that presents experimental devices that allow us to detect individual quantum systems and observe quantum jumps occurring at random times. Described: superconducting single photon detectors, detection of arrays of ions and atoms, the shelving technique that allows us to measure the quantum state of the single atom, state selective field ionization of single Rydberg atoms, detection of single molecules on a surface by confocal microscopy, articial atoms in circuit quantum electrodynamics (cQED)
Continuous measurements play a pivotal role in the study of dynamical open quantum systems. ``Dyne'' detections are among the most widespread and efficient measurement schemes, and give rise to quantum diffusion of the conditioned state. In this work we study under what conditions the detector dependency of the conditional state of a quantum system subject to diffusive monitoring can be demonstrated experimentally, in the sense of ruling out any detector-independent pure-state dynamical model for the system. We consider an arbitrary number L of environments to which the system is coupled, and an arbitrary number K of different types of dyne detections. We prove that nontrivial necessary conditions for such a demonstration can be determined efficiently by semidefinite programming. To determine sufficient conditions, different physical environmental couplings and Hamiltonians for a qubit and different sets of diffusive monitorings are scrutinized. We compare the threshold efficiencies that are sufficient in the various cases, as well as cases previously considered in the literature, to suggest the most feasible experimental options.
Abstract The dynamics of Gaussian states for open quantum systems described by Lindblad equations can be solved analytically for systems with quadratic Hamiltonians and linear Lindbladians, showing the familiar phenomena of dissipation and decoherence. It is well known that the Lindblad dynamics can be expressed as an ensemble average over stochastic pure-state dynamics, which can be interpreted as individual experimental implementations, where the form of the stochastic dynamics depends on the measurement setup. Here we consider quantum-jump and stochastic Schrödinger dynamics for initially Gaussian states. While both unravellings converge to the same Lindblad dynamics when averaged, the individual dynamics can differ qualitatively. For the stochastic Schrödinger equation, Gaussian states remain Gaussian during the evolution, with stochastic differential equations governing the evolution of the phase-space centre and a deterministic evolution of the covariance matrix. In contrast to this, individual pure-state dynamics arising from the quantum-jump evolution do not remain Gaussian in general. Applying results developed in the non-Hermitian context for Hagedorn wavepackets, we formulate a method to generate quantum-jump trajectories that is described entirely in terms of the evolution of an underlying Gaussian state. To illustrate the behaviours of the different unravellings in comparison to the Lindblad dynamics, we consider two examples in detail, which can be largely treated analytically, a harmonic oscillator subject to position measurement and a damped harmonic oscillator. In both cases, we highlight the differences as well as the similarities of the stochastic Schrödinger and the quantum-jump dynamics.
A number of experiments on trapped single ions or atoms have been performed in recent years [1,2,3,4]. Monitoring the intensity of scattered laser light off of such systems has shown abrupt changes that have been cited as evidence of between states of the scattered ion or atom . The existence of such jumps was required by Bohr in his theory of the atom. Bohr’s quantum jumps between atomic states [5] were the first form of quantum dynamics to be postulated. He assumed that an atom remained in an atomic eigenstate until it made an instantaneous jump to another state with the emission or absorption of a photon. Since these jumps do not appear to occur in solutions of the Schrodinger equation, something similar to Bohr's idea has been added as an extra postulate in modern quantum mechanics. Stochastic quantum jump equations [6], [7],[8]were introduced as a tool for simulating the dynamics of a dissipative system with a large Hilbert space and their links with quantum measurement the or were also noted [9],[10],[11],[12],[13].This measurement interpretation is generally known as quantum trajectory theory [14].By adding filter cavities as part of the apparatus, even the quantum jumps in the dressed state model can be interpreted as approximations to measurement-induced jumps [15]. The question arises whether an explanation of these jumps can be found to result from an Colombeau solution [16]-[18](Ψe(x, t;ħ))e of the Schrodinger equation alone without additional postulates. We found exact quasi-classical asymptotic of the quantum averages
A microscopic system under continuous observation exhibits at random times sudden jumps between its states. The detection of this essential quantum feature requires a quantum non-demolition (QND) measurement1, 2, 3 repeated many times during the system evolution. Quantum jumps of trapped massive particles (electrons, ions or molecules4,5,6,7,8) have been observed, which is not the case of the jumps of light quanta. Usual photodetectors absorb light and are thus unable to detect the same photon twice. They must be replaced by a transparent counter 'seeing' photons without destroying them3. Moreover, the light has to be stored over a duration much longer than the QND detection time. We have fulfilled these challenging conditions and observed photon number quantum jumps. Microwave photons are stored in a superconducting cavity for times in the second range. They are repeatedly probed by a stream of non-absorbing atoms. An atom interferometer measures the atomic dipole phase shift induced by the non-resonant cavity field, so that the final atom state reveals directly the presence of a single photon in the cavity. Sequences of hundreds of atoms highly correlated in the same state, are interrupted by sudden state-switchings. These telegraphic signals record, for the first time, the birth, life and death of individual photons. Applying a similar QND procedure to mesoscopic fields with tens of photons opens new perspectives for the exploration of the quantum to classical boundary9, 10.